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Home  >>  CBSE XII  >>  Math  >>  Determinants
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If $\Delta = \begin{vmatrix} a_11&a_12&a_13 \\ a_21&a_22&a_23 \\ a_31&a_32&a_33 \end{vmatrix} $ and $A_y$ is Cofactor of $a_y$, then value of $\Delta$ is:

\[ \begin{array}{l} (A) \quad a_{11}A_{31}+a_{12}A_{32}+a_{13}A_{33} & (B) \quad a_{11}A_{11}+a_{12}A_{21}+a_{13}A_{31} \\(C) \quad a_{21}A_{11}+a_{22}A_{12}+a_{23}A_{13} & (D) \quad a_{11}A_{11}+a_{21}A_{21}+a_{31}A_{31} \\\end{array} \]
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1 Answer

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  • $\bigtriangleup$ of a determinant is the sum of the product of the element of a column (or a row)with its corresponding cofactors.
We know that $\bigtriangleup$=Sum of the product of the element of a column (or a row) with its corresponding cofactors.
Hence $\bigtriangleup=a_{11}A_{11}+a_{21}A_{21}+a_{31}A_{31}$
Hence the correct answer is D.


answered Feb 24, 2013 by sreemathi.v
edited Feb 28, 2013 by vijayalakshmi_ramakrishnans

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